Recent NA48/2 results on QCD and ChPT

The NA48/2 experiment at CERN collected a very large sample of charged kaon decays into multiple final states.This data allow measurements related to QCD and Chiral Perturbation Theory (ChPT). In particular, we collected about 1500 events of the very rare decay $K^{\pm} \rightarrow \mu^{\pm} \nu e^+ e^-$ over almost negligible background in the region with m(e$^+$e$^-$) above 140 MeV, which is of great interest in Chiral Perturbation Theory, thanks to the $m_{ee}$ spectrum and a model-independent measurement of the decay rate for this region. Also we performed the first observation of the rare decay $K^+ \rightarrow \pi^+ \pi^0 e^+ e^-$, with about 5000 candidates and 5% background contamination, and the preliminary branching ratio in the full kinematic region has been measured, in perfect agreement with theoretical predictions based on Chiral Perturbation Theory. Finally, we obtained our final measurement of the charged kaon semileptonic decays form factors based on 4.28 million $K^{\pm} e3$ and 2.91 million $K^{\pm} \mu3$ selected decays, with the smallest uncertainty for $K^{\pm} e3$ and a competitive result for $K^{\pm} \mu3$ and leading to the most precise combined $K^{\pm} l3$ result that reduces the form factor uncertainty of $\lvert V_{us} \rvert$.